Model 2 Train Vs Train in opposite direction Section-Wise Topic Notes With Detailed Explanation And Example Questions

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The following question based on trains topic of quantitative aptitude

Questions : Two trains of length 137 metre and 163 metre are running with speed of 42 km/hr and 48 km/hr respectively towards each other on parallel tracks. In how many seconds will they cross each other?

(a) 24 sec

(b) 12 sec

(c) 10 sec

(d) 30 sec

The correct answers to the above question in:

Answer: (b)

Using Rule 3,

Relative speed

= 42 + 48 = 90 kmph

= $({90 × 5}/18)$ m/s = 25 m/s

Sum of the length of both trains

= 137 + 163 = 300 metres

Required time = $300/25$ = 12 seconds

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Read more trains in opposite direction Based Quantitative Aptitude Questions and Answers

Question : 1

A train, 150m long, passes a pole in 15 seconds and another train of the same length travelling in the opposite direction in 12 seconds. The speed of the second train is

a) 48 km/hr

b) 52 km/hr

c) 54 km/hr

d) 45 km/hr

Answer: (c)

Using Rule 3,

Let the speed of the second train be x m/s

Speed of first train

= $150/15$ = 10 m/sec

Relative speed of trains

= (x + 10) m/s

Total distance covered

= 150 + 150 = 300 metre

Time taken = $300/{x + 10}$

$300/{x + 10}$ = 12

12x + 120 = 300

12x = 300 - 120 = 180

x = $180/12$ = 15 m/s

= ${15 × 18}/5$ or 54 kmph.

Question : 2

Two places P and Q are 162 km apart. A train leaves P for Q and simultaneously another train leaves Q for P. They meet at the end of 6 hours. If the former train travels 8 km/hour faster than the other, then speed of train from Q is

a) 10$5/6$ km/hour

b) 9$1/2$ km/hour

c) 8$1/2$ km/hour

d) 12$5/6$ km/hour

Answer: (b)

Speed of train starting from Q = x kmph

Speed of train starting from P = (x + 8) kmph

According to the question,

PR + RQ = PQ

(x + 8) × 6 + x × 6 = 162

[Distance = Speed × Time]

6x + 48 + 6x = 162

12x = 162 - 48 = 114

x = $114/12 = 19/2 = 9{1}/2$ kmph

Question : 3

Two towns A and B are 500 km. apart. A train starts at 8 AM from A towards B at a speed of 70 km/ hr. At 10 AM, another train starts from B towards A at a speed of 110 km/hr. When will the two trains meet ?

a) 12 Noon

b) 12.30 PM

c) 1.30 PM

d) 1 PM

Answer: (a)

Let two trains meet after t hours when the train from town A leaves at 8 AM.

Distance covered in t hours at 70 kmph

+ Distance covered in (t - 2) hours at 110 kmph = 500km

70t + 110 (t - 2) = 500

70t + 110t - 220 = 500

180 t = 500 + 220 = 720

t = $720/180$ = 4 hours

Hence, the trains will meet at 12 noon.

Question : 4

Two trains 108 m and 112 m in length are running towards each other on the parallel lines at a speed of 45 km/hr and 54 km/ hr respectively. To cross each other after they meet, it will take

a) 9 sec

b) 8 sec

c) 10 sec

d) 12 sec

Answer: (b)

Using Rule 3,

Relative speed

= 45 + 54 = 99 kmph

= $(99 × 5/18)$ m/sec. or $55/2$ m/sec.

Required time = ${108 + 112}/{55/2}$

= ${220 × 2}/55 = 8$ seconds

Question : 5

The distance between two cities A and B is 330 km. A train starts from A at 8 a.m. and travels towards B at 60 km/hr. Another train starts from B at 9 a.m. and travels towards A at 75 km/hr. At what time do they meet?

a) 10 : 30 a.m.

b) 11 a.m.

c) 11 : 30 a.m.

d) 10 a.m.

Answer: (b)

Distance travelled by first train in one hour

= 60 × 1 = 60km

The given distance between two cities A and B is 330 km.

Therefore, distance between two train at 9 a.m.

= 330 - 60 = 270 km

Now, Relative speed of two trains

= 60 + 75 = 135 km/hr

Time of meeting of two trains

= $270/135$ = 2 hrs.

Therefore, both the trains will meet at

9 + 2 = 11 A.M.

Question : 6

Two trains X and Y start from Jodhpur to Jaipur and from Jaipur to Jodhpur respectively. After passing each other they take 4 hours 48 minutes and 3 hours 20 minutes to reach Jaipur and Jodhpur respectively. If X is moving at 45 km/hr, the speed of Y is

a) 58 km/hr

b) 54 km/hr

c) 64.8 km/hr

d) 60 km/hr

Answer: (b)

Using Rule 11,Two trains A and B, run from stations X to Y and from Y to X with the speed '$S_A$' and '$S_B$' respectively. After meeting with each other. A reached at Y after '$t_A$' time and B reached at X after '$t_B$' time. Then Ratio of speeds of trains,$S_A/S_B = √{t_B/t_A}$

 

$\text"Speed of X"/\text"Speed of Y"$

= $√\text"Time taken by Y"/\text"Time taken by X"$

$45/y = √\text"3 hours 20 min"/\text"4 hours 48 min"$

$45/y = √\text"200 minutes"/\text"288 minutes" = 10/12$

10y = 12 × 45

$y = {12 × 45}/10$ = 54 kmph

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